4 A + 2 B = 28
5 A + 3 B = 37
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
4 A + 2 B = 28 --- (1)
5 A + 3 B = 37 --- (2)
(2) - (1)
(5 A + 3 B) - (4 A + 2 B) = 37 - 28
5 A - 4 A + 3 B - 2 B = 9
1 A + 1 B = 9 --- (3)
1 A + 1 B = 9
(b)
Make B the same.
LCM of 1 and 2 = 2
(3) x 2
2 A + 2 B = 18 --- (4)
(1) - (4)
(4 A + 2 B) - (2 A + 2 B) = 28 - 18
4 A - 2 A + 2 B - 2 B = 10
2 A = 10
1 A = 10 ÷ 2 = 5
(c)
Substitute 1 A = 5 into (3).
1 A + 1 B = 9
5 + 1 B = 9
1 B = 9 - 5 = 4
Answer(s): (a) 9; (b) 5; (c) 4